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I've got some engine vibrations when running idle. Not sure if engine should vibrate like this or not
The vibration's frequency is quite high, hard to capture on video. Instead, you only see the engine cover moving slowly in the video. But in fact it vibrates very quickly

When removing the cover, the engine itself vibrates even quicker, so on video it looks still.

... I've got some engine vibrations when running idle. Not sure if engine should vibrate like this or not
The vibration's frequency is quite high, hard to capture on video. Instead, you only see the engine cover moving slowly in the video. But in fact it vibrates very quickly

When removing the cover, the engine itself vibrates even quicker, so on video it looks still.

I wonder what the cause might be and where to start looking for it.

No M47 engines here in the USA, there are a few UK guys here. Have you posted on the UK site?

But, I don't think there's anything wrong with the engine itself. 4-pot engines are rougher running than i-6, and it looks and sounds pretty much normal.

Two things I can think of to check:
1) Engine mount may be broken; this would cause engine vibrations to be not damped. However problems with them usually are apparent while under load (on road).
2) I believe that the M47 has a mass damper (counterweight system) to smooth vibrations of the I-4. However, it's gear-driven and I think if it failed the engine might not run...

Two things are the causes for your concern:
1. Engine cover isn't secured completely (reinspect all rubber mounting grommets under the cover and their metal contact points on the engine)
2. The engine has four cylinders

The 320d has a known issue with failure of the front pulley assembly, which includes a mass dampener. I am not sure if this also applies to the 318d. The problem was mostly for Diesel E46 models, but apparently some E90 models also had this problem. Anyway, you may want to get that checked.

...alpinweiss (my favorite bmw color): I read about E46 problem with mass dampner. I think it can be inspected visually from under the car, right?

Thank you for the compliment.

Yes, you can see the engine pulley and vibration damper from below. You will have to remove the protective cover underneath. But I am not sure if you will be able to see if it has failed, or not. Obviously, if the rubber has completely decomposed, you should be able to see it, but if it is a fine crack, it may not be as easy to see. You may have to physically test the damper.